Can I copy UV map to many objects with the same and/or symmetrical topology?
I used the suggestion given by gandalf3 and made it all work for my case. Here is the procedure:


I have 14 shoes objects with identical broken UV, 7 of them are mirrored (using CtrlM mesh mirroring).
I fix UV on one of the shoes
I go to its mirrored version of the fixed shoe, flip normals and then use CtrlL -> Transfer UV layouts. (If I do not flip normals transfer does not work right and resulting texture is a mess).
I flip normals on the mirrored object again. At this point one size of the shoes has right texture with correct UV map for both mirrored and not mirrored mesh.
I use mirrored mesh to transfer to all 7 mirrored sizes  by selecting all mirrored objects and selecting last the mirrored object with corrected UV and using CtrlL -> Transfer UV layouts.
Repeat the same procedure for not mirrored 7 sizes.